4c88-8c25-e0fa397adoe0/assignment/91b3de91-51e1-4282-9dfb-ba46cfdeaferd BACK TO

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4c88-8c25-e0fa397adoe0/assignment/91b3de91-51e1-4282-9dfb-ba46cfdeaferd BACK TO ASSIGNMENT OVERVIEW Applications Using the Definition of the Derivative Solve Application Problems Using the Definition of the Derivative Question velocities of the car over several time intervals. Use this table to estimate the instantaneous velocity at t 5. The position in feet of a car along a straight road after t seconds is modeled by s(t) 14t2. Below is a table of average Interval 0 aug 5,5.1 141.4 5,5.01 140.14 5,5.0011 140.014 5,5.0001 140.0014 15,5.00001 140.00014 Do not include units in your answer.

Explanation / Answer

From the given table, we can see that as we shorten the interval of time the average velocity gets closer to 140. Average velocity between the times t = 5 and t = 5.00001 is 140.00014 feet per seconds.

Instantaneous velocity is the velocity at exactly t = 5, that is the difference between the times should be negligible while using average velocity for estimating instantaneous velocity. As the difference between the times get neglibible, the average velocity will have almost 140 feet per second.

Therefore, instantaneous velocity of the car will be 140.

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